Comparison among algorithms for sequencing runs of the full 2<SUP align="right">n</SUP> factorial experiment

Abstract

The complete 2n factorial experiment has 2n different experimental runs among which there are 2n! permutations for carrying out this experiment sequentially one run at a time, but not all of these permutations produce runs sequences with desirable properties. There are four algorithms for sequencing runs of the 2n factorial experiment such that: 1) main effects and/or two-factor interactions are orthogonal to the linear/quadratic time trend and/or such that; 2) the total number of factor level changes between the 2n runs (i.e., the cost) is minimal. These algorithms are: Correa et al. (2009), Cui and John (1998), Cheng and Jacroux (1988) and Coster and Cheng (1988), referred to here as Algorithms 1, 2, 3(a) and 3(b) and 4, respectively. This paper conducts a comparison among these algorithms and documents their differences according to the three criteria: 1) which algorithm produces runs sequences in a less number of factor level changes (i.e., less costly); 2) which algorithm produces runs sequences with more linear/quadratic time trend free main effects and/or two-factor interactions; 3) which runs sequence of an algorithm can be generated by another algorithm using the generalised fold-over scheme or the interactions-main effects assignment. Results of this comparison are summarised in Section 4.